Disasters can disrupt road networks by blocking some of the roads and consequently impeding accessibility to critical locations. In the immediate post-disaster response phase, while the blockage information is yet to be collected, relief distribution crews (RDCs) should dispatch from warehouses to supply critical locations with first aid items. The RDCs are not capable of unblocking damaged roads and should find a way to bypass them once such edges are observed in their routes. With the objective of minimizing total latency of the critical nodes, we study the problem that addresses the relief distribution operations with $k$ non-recoverable online blocked edges. The online blocked edges are not known to the RDCs initially and the blockage of a blocked edge is revealed when one of the RDCs arrives at one of its end-nodes. Once one of the RDCs knows about a blocked edge, this information is communicated among the rest of the RDCs and they will all be informed about that blocked edge. We first investigate the worst-case performance of online algorithms against offline optimal solutions using competitive ratio. We then prove a lower bound on the competitive ratio of deterministic online algorithms. We also provide an upper bound on the competitive ratio of the optimal deterministic online algorithms by introducing a deterministic algorithm which achieves a bounded competitive ratio. We then develop three heuristic algorithms to solve this problem. One of our algorithms is based on solving an Integer Programming model to find the assignment of the nodes to the RDCs and then finding the routes dynamically. The other algorithms are not based on solving optimization models and hence are more efficient in terms of their computational time. We compare our proposed heuristic algorithms with the best known algorithms from the literature that are developed for a single RDC variation of the problem. Finally, we provide a through computational analysis of our algorithms on instances adopted from real-world road networks.

灾害可以通过阻塞一些道路并因此阻碍关键地点的可达性来破坏道路网络。在灾后应急响应阶段，在尚未收集到堵塞信息的情况下，救援配送人员 (RDC) 应从仓库派遣到关键地点提供急救物品。RDC 无法疏通损坏的道路，一旦在其路线中观察到此类边缘，就应该找到绕过它们的方法。为了最小化关键节点的总延迟，我们研究了解决救济分发操作的问题$克$不可恢复的在线阻塞边缘。RDC 最初不知道在线阻塞边缘，并且当 RDC 之一到达其端节点之一时，会显示阻塞边缘的阻塞。一旦其中一个 RDC 知道被阻塞的边缘，该信息就会在其余 RDC 之间进行通信，并且它们都将被告知该被阻塞的边缘。我们首先使用竞争比率研究在线算法相对于离线最优解的最坏情况性能。然后，我们证明了确定性在线算法的竞争比率的下限。我们还通过引入实现有界竞争比率的确定性算法，提供了最优确定性在线算法的竞争比率的上限。然后我们开发了三种启发式算法来解决这个问题。我们的算法之一是基于求解整数规划模型来查找节点到 RDC 的分配，然后动态查找路由。其他算法不基于求解优化模型，因此在计算时间方面更有效。我们将我们提出的启发式算法与文献中为问题的单个 RDC 变体开发的最著名的算法进行了比较。最后，我们对从现实世界道路网络采用的实例的算法进行了计算分析。我们将我们提出的启发式算法与文献中为问题的单个 RDC 变体开发的最著名的算法进行了比较。最后，我们对从现实世界道路网络采用的实例的算法进行了计算分析。我们将我们提出的启发式算法与文献中为问题的单个 RDC 变体开发的最著名的算法进行了比较。最后，我们对从现实世界道路网络采用的实例的算法进行了计算分析。